(Reuters) - Texas Governor Greg Abbott made good on his promise to cut $1.5 million in grant money to Travis County after the county sheriff said she would limit her department's cooperation with federal immigration officers, county officials said on Wednesday.

Travis County includes the Texas capital Austin, which is a so-called "sanctuary city".

Abbott spokeswoman Ciara Matthews said the money that would be withheld from Travis County is a series of one-time criminal justice grants totaling $1.8 million. About $300,000 of that has already been spent, but she said the governor would not try to claw back that money.

Sanctuary cities in general offer safe harbor to illegal immigrants and often do not use municipal funds or resources to advance the enforcement of federal immigration laws. Sanctuary city is not an official designation.

In January, newly elected Sheriff Sally Hernandez said in a statement on the Sheriff's Office website that she was "following all state and federal laws, and upholding constitutional rights to due process for all in our criminal justice system. Our community is safer when people can report crimes without fear of deportation."

In a Jan. 20 memo seen by Reuters, her office said it would make an exception for people charged with serious crimes like murder, aggravated sexual assault, or human smuggling.

Hernandez was not available to comment on Wednesday.

Travis County Judge Sarah Eckhardt, who manages the county's budget, said on Wednesday that Hernandez's directive does not violate state or federal law.

"Any of the 254 sheriffs across the state of Texas has discretion to decide whether or not to put their resources toward assisting federal immigration enforcement," she said in a press conference that was webcast.

"I will do everything I can to protect revenue sources. I believe it is foolhardy for the state to starve itself by starving its own programs," she said.

In a letter to Hernandez in January, Abbott said her position was "not a pronouncement of sound public policy; it is a dangerous game of political Russian roulette – with the lives of Texans at stake."

Abbott has voiced strong support for proposed legislation in Texas that would penalize sanctuary cities.

On Tuesday, San Francisco, another sanctuary city, filed a lawsuit challenging a Jan. 25 executive order by President Donald Trump directing the U.S. government to withhold money from cities that have adopted sanctuary policies toward illegal immigrants.

The lawsuit marked the first court challenge over the sanctuary order.

New York, Los Angeles, Chicago, Philadelphia, Boston, Denver, Washington and Seattle, in addition to San Francisco, offer forms of protection to illegal immigrants, and billions of dollars in federal aid to those cities could be at risk.

(Reporting by Rory Carroll in San Francisco; Editing by Toni Reinhold)